# Circle

A circle is a basic geometric shape that is useful throughout mathematics. It is defined a shape where every point along its perimeter is an equal distance from its center.

Property | Image | Description |
---|---|---|

Radius | The radius is the distance from the center of the circle to any point along the perimeter of the circle. | |

Circumference | The circumference, denoted with the variable , is the length around the perimeter of the circle. | |

Diameter | The diameter is the distance between any two points along the perimeter of the circle that passes through the center of the circle. | |

Area | The area of a circle is the amount of two-dimensional space that fits inside the perimeter of the circle. |

The area of a circle is give by one-half multiplied by τ (tau) mutliplied by the radius of the circle squared.

The circumference of a circle is given the constant τ (tau) multpilied by the radius of the circle, where τ = 2π.

The standard form of a circle is given by the radius and center point of the circle.

The standard form of the equation of a circle is given in terms of its radius and center point.

Radians are a unit that measure angle using the radius of a circle. One radian is equal to the amount of rotation required to travel the length of one radius along the circumference of the circle.

Degrees is a unit of measure for angles. A full rotation is equal to 360 degrees. In the cartesian coordinate system, degrees are measured starting from the rightmost edge of the circle.

The unit circle is a unifying idea in mathematics that connects many useful concepts together. This article goes over the basic properties of the circle using interactive examples and explains how they connect to the trigonometric functions and pythagorean theorem.